Simplify the following expression: $r = \dfrac{9y^2 + 81y + 180}{y + 5} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ r =\dfrac{9(y^2 + 9y + 20)}{y + 5} $ Then we factor the remaining polynomial: $y^2 + {9}y + {20} $ ${5} + {4} = {9}$ ${5} \times {4} = {20}$ $ (y + {5}) (y + {4}) $ This gives us a factored expression: $\dfrac{9(y + {5}) (y + {4})}{y + 5}$ We can divide the numerator and denominator by $(y - 5)$ on condition that $y \neq -5$ Therefore $r = 9(y + 4); y \neq -5$